Dynamical Cobordism Conjecture: solutions for end-of-the-world branes
Ralph Blumenhagen, Christian Kneißl, Chuying Wang
Abstract
A bstract We analyze finite size solutions for a generalized D -dimensional Dudas-Mourad (DM) model featuring dynamical cobordism with neutral and charged end-of-the-world (ETW) defect branes. Confirming a dynamical version of the Cobordism Conjecture, we explicitly construct non-isotropic solutions for the latter codimension one branes and show the appearance of a lower bound $$ \delta \ge 2\sqrt{\left(D-1\right)/\left(D-2\right)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>δ</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>2</mml:mn> <mml:msqrt> <mml:mrow> <mml:mfenced> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:mfenced> <mml:mo>/</mml:mo> <mml:mfenced> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>−</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:msqrt> </mml:math> for the critical exponent in the scaling behavior of the distance and the curvature close to the wall. This allows us to make a connection to the (sharpened) Swampland Distance Conjecture and the (Anti-) de Sitter Distance Conjecture. Moreover, BPS orientifold planes appear as special cases in our analysis and the whole picture is consistent with dimensional reduction from ten to D dimensions. An analogous analysis is performed for a generalized Blumenhagen-Font (BF) model featuring neutral codimension two ETW-branes where the same lower bound for the scaling parameter δ arises.